cc - after your help over in Cafe Society, I wanted to be sure and pipe in with my “tooter” application thoughts. (ouch - sorry, won’t happen again)
Anyway, yes, at this point you should be persistent, but no, at this point, you should not show up in person. You need to:
a) call and gently, nicely, persistently talk to receptionists and folks until to you identify the right person or department who should be reviewing your resume and potentially interviewing you. If people are not helpful, try stuff like “given my background, it sounds like I am uniquely able to help you guys out - so I want to make sure I am talking to the person on point, who sees that on my resume” or some such.
b) if the you either reach the person, or maybe even better, reach someone who sounds like they know exactly who the right person is and are about to refer you to them, then - ask them for advice. “Wow, so Steve is the right person? Great - and what is his contact info and email? Cool - thanks. And if I want to show him that I am a great fit and really, really interested in the position, how should I do that - d’you think I should give him a call, send him an email or show up? If I should show up, about what time of day would be best?” etc…
Most people like being asked for their expertise - make sure you sound enthusiastic and appreciative - it will get you places you couldn’t get otherwise.
Best of luck!